Preheat the oven to 180 C / Gas 4. Rub a gratin dish with the cut side of the peeled garlic clove, then rub with some butter.
Place the potato slices in a bowl, add 30g of the grated Gruyere cheese, the 2 crushed garlic cloves, parsley, salt, pepper and nutmeg. Stir to mix well. Spread the mixture into the prepared gratin dish.
Bring the milk to the boil in a saucepan, then whisk in the crème fraîche. Strain the mixture through a sieve. Pour over the potatoes, sprinkle with the remaining Gruyère cheese and dot with the 40g butter.
Bake in the preheated oven until the top is golden and the centre is bubbly, about 45 minutes. Place a sheet of aluminium foil over the dish if the top is browning too quickly. Turn off the oven, and leave in the oven for 10 minutes to rest before serving.